Handbook of Dynamical Systems

In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli.

Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systemsHighlights developments that are the foundation for future research in this fieldProvides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems

1. Introduction, 2. Complex linearization, 3. KAM Theory for circle and annulus maps, 4. KAM Theory for flows, 5. Further developments in KAM Theory, 6. Quasi-periodic bifurcations: dissipative setting, 7. Quasi-periodic bifurcation theory in other settings, 8. Further Hamiltonian KAM Theory, 9. Whitney smooth bundles of KAM tori, 10. Conclusion